The goal, specifically, is if we were to consider new variables a_ij = y_i-z_j, we want to express the polynomial with nonnegative coefficients in terms of these variables. Since the variables are not linearly independent, a change of variables won't necessarily work, and my code uses linear optimization.

The goal, specifically, is if we were to consider new variables a_ij = y_i-z_j, we want to express the polynomial with nonnegative integer coefficients in terms of these variables. Since the variables are not linearly independent, a change of variables won't necessarily work, and my code uses linear optimization.

(y_1 - z_1)*(y_3 - z_2) + (y_2 - z_1)*(y_1 - z_2)

(y_1 - z_1)*(y_3 - z_2) + (y_2 - z_1)*(y_1 - z_3)